Mobilities of two spherical particles immersed in a magneto-micropolar fluid

In this article, we consider the slow quasi-steady translational motion of two spherical particles immersed in an unbounded magneto-micropolar fluid. The micropolar fluid is allowed to slip and spin slip at the surfaces of the particles. The two particles are of the same material and may differ in radius. The particles migrate along the line connecting their centers with different velocities (or indifferent applied forces). The solutions are found under the conditions of low Reynolds numbers. The governing differential equations are solved semi-analytically in conjunction with the boundary collocation techniques. The interaction effects between the particles are evaluated through the magneto-micropolar mobility coefficients. Values of the mobility coefficients are tabulated and represented graphically and then discussed for various values of the relevant parameters. In general, it is found that the effect of the micropolarity parameter with the magnetic Hartmann number is significant. The convergence and accuracy of our collocation scheme for the normalized drag force acting on each particle for different values of spacing distance and Hartmann number is shown in Table 1. Results of the normalized drag force agree very well with the existing solutions in the absence of the transverse magnetic field, which was published in the work of Sherief et al., "Interaction between two rigid spheres moving in a micropolar fluid with slip surfaces," J. Mol. Liq. 290, 111165 (2019) and, also for the case of Newtonian fluid, was published in the work of Shreen and Alsudais, "Effect of magnetic field on the motion of two rigid spheres embedded in porous media with slip surfaces," Eur. Phys. J. E 44, 1 (2021). Published under an exclusive license by AIP Publishing.